Well I would not dream of not using the BS model before buying a warrant or option. no questione.
As far as VI goes, you do need the historical price.
ype 1: Historical Volatility
Volatility in its most basic form represents daily changes in stock prices. We call this historical volatility (or historic volatility) and it is the starting point for understanding volatility in the greater sense. Historic volatility is the standard deviation of the change in price of a stock or other financial instrument relative to its historic price over a period of time. That sounds quite eloquent but for the average investor who does not command an intimate knowledge of statistics, the definition is most overwhelming
thestreet.com
Volatility and Options
Volatility is one of the many important inputs -- along with market price, strike price, interest rates, dividends and time -- in calculating the value of an option. The most popular options pricing model is Black-Scholes. If you desire to torture yourself with how the Black-Scholes options pricing model works, I have provided a link for further reference. When calculating an option price, one merely inputs the volatility as a given for the reference security (underlying security, in options speak) for a period of time to match the remaining days to expiration, along with the other required variables, into the Black-Scholes model, and out pops the option valuation.
ivolatility.com
The binomial option pricing model
First proposed by Cox, Ross and Rubinstein in a paper published in 1979, the binomial model to price an option is probably the most common model used for equity calls and puts today.
The model divides the time to an option’s expiry into a large number of intervals, or steps. At each interval it calculates that the stock price will move either up or down with a given probability and also by an amount calculated with reference to the stock’s volatility, the time to expiry and the risk free interest rate. A binomial distribution of prices for the underlying stock or index is thus produced.
At expiry the option values for each possible stock price are known as they are equal to their intrinsic values. The model then works backwards through each time interval, calculating the value of the option at each step. At the point where a dividend is paid (or other capital adjustment made) the model takes this into account. The final step is at the current time and stock price, where the current theoretical fair value of the option is calculated.
The number of steps in the model determines its speed, however most home PCs today can easily handle a model with 100 or so steps, which gives a sufficient level of accuracy for calculating a theoretical fair value.
The Black-Scholes model
First proposed by Black and Scholes in a paper published in 1973,the so called Black-Scholes model is an analytic solution to price a European option on a non dividend paying asset. It formed the foundation for much theory in derivatives finance. The Black-Scholes formula is a continuous time analogue of the binomial model.
The Black-Scholes formula uses the pricing inputs to analytically produce a theoretical fair value for an option. The model has many variations which attempt, with varying levels of accuracy, to incorporate dividends and American style exercise conditions. However with computing power these days the binomial solution is more widely used.
Volatility
The volatility figure input into an option pricing model reflects the assumptions of the person using the pricing model. Volatility is defined technically in various ways, depending on assumptions made about the underlying asset’s price distribution. For the regular warrant trader it is sufficient to know that the volatility a trader assigns to a stock reflects expectations of how the stock price will fluctuate over a given period of time.
Volatility is usually expressed in two ways: historical and implied.
Historical volatility
Historic volatility describes volatility observed in a stock over a given period of time. Price movements in the stock (or underlying asset) are recorded at fixed time intervals (for example every day, every week, or every month) over a given period. More data generally leads to more accuracy.
Be aware that a stock’s past volatility may not necessarily be reproduced in the future. Caution should be used in basing estimates of future volatility on historical volatility. In estimating future volatility, a frequently used compromise is to assume that volatility over a coming period of time will be the same as measured/historical volatility for that period of time just finished. Thus if you want to price a three month warrant, you may use three month historical volatility.
Implied volatility relates to the current market for a warrant. Volatility is implied from the warrant’s current price, using a standard option pricing model. Keeping all other inputs constant, you can put the current market price of a warrant into any theoretical option price calculator and it will calculate the volatility implied by that warrant price.
This is one of the key figures traders watch to assist them in assessing the value of an option. It is also commonly fed back into the option pricing model to calculate the warrant’s theoretical fair value.
* Black-Scholes analysis (no dividends)
* Black-Scholes analysis (with dividends)
* Warrants binomial model calculator
Technical Studies: Volatility
The Volatility indicator plots a moving average of a security's standard deviation over a specified time period. It indicates the extent to which the security's price has fluctuated from its average price during that period.
The default parameter is 20 minutes/hours/days/weeks/months, depending on the selected frequency. Twenty (20) is the default period given that 20 trading days is roughly equivalent to one month. The parameter can be customized to plot the standard deviation line over shorter or longer periods.
Interpreting Volatility: According to some technical analysts, "The bigger the base, the bigger the move." Essentially, periods of low volatility (tighter trading ranges) often precede periods of high volatility, or large price swings. And those swings may occur either upward or downward.
The standard deviation line rises when fluctuations in a security's price are at their wildest. This often occurs soon after the security breaks above or below a trading range. In contrast, the standard deviation line is lowest when the security's trading range tightens and prices are relatively stable. The bigger the gap between the closing prices and the average price over the period, the higher the standard deviation line. Conversely, the closer the gap between the closing prices and average price over the period, the lower the standard deviation line.
Calculating Volatility: To calculate Volatility, start by finding the variance.
Variance = Sum of all deviations from the mean, squared, for last n closing prices / n
Where the default value for n is 20, but can be customized.
For a 20-day standard deviation, for example, the average closing price during the 20-day period might be 40.90 while the 20th day's closing price is 38.90. The deviation from the moving average for the twentieth day is -2. The square of -2 is 4. Add that number to the square of the deviation for the previous 19 remaining periods and divide the sum by 20 to arrive at the variance.
Then calculate the standard deviation:
n-period Standard Deviation = Square root of Variance
If Variance = 4.5, then the n-period Standard Deviation = 2.12
Standard Deviation and trading ranges: The standard deviation can be used to determine an expected trading range of a security over a specified time period. A 20-day standard deviation of 2.12 means the security, in all likelihood, stayed within a range of plus-or-minus $2.12 of its average price 66% of the time during the past 20 trading days. If the security's average price during the period was $45, for example, we would expect the security to stay within a range of $42.88 and $47.12 during the period 66% of the time.
Similarly, we'd also expect the security to stay within two standard deviations of its average price 95% of the time within the period. Two standard deviations of $2.12, which is 2 x $2.12, is $4.24. So 95% of the time during the 20-day period, we'd expect the security to stay above $40.76 and below $49.24. |
